The spontaneity means having the potential to proceed without assistance of external agency. The processes which occur spontaneously are

Options

A. flow of heat from colder to warmer body
B. gas in a container contracting into one corner
C. gas expanding to fill the available volume
D. burning carbon in oxygen to give carbon dioxide

Explanation

To determine which processes occur spontaneously, we need to analyze each option based on the definition of spontaneity, which is the ability of a process to occur without the assistance of an external agency. Let's go through the options step by step.

### Step-by-Step Solution:

1. **Understanding Spontaneity**:
- Spontaneous processes are those that can occur naturally without any external influence. This means they can proceed on their own once initiated.

2. **Analyzing Option A**:
- **Flow of heat from colder to warmer body**:
- This process is not spontaneous. Heat naturally flows from a warmer body to a colder body due to the second law of thermodynamics. Therefore, this option is incorrect.

3. **Analyzing Option B**:
- **Gas in a container contracting in one corner**:
- Gases naturally expand to fill the entire volume of their container. For a gas to contract, external pressure must be applied. Thus, this process is also not spontaneous, making this option incorrect.

4. **Analyzing Option C**:
- **Gas expanding to fill the available volume**:
- This process is spontaneous. When gas is placed in a container, it will naturally spread out to occupy the entire volume available to it without any external assistance. Therefore, this option is correct.

5. **Analyzing Option D**:
- **Burning of carbon in oxygen to give carbon dioxide**:
- This combustion reaction is spontaneous once initiated. After the initial ignition, the reaction continues on its own without needing further assistance. Hence, this option is also correct.

### Conclusion:
Based on the analysis:
- **Correct Options**: C (Gas expanding to fill the available volume) and D (Burning of carbon in oxygen to give carbon dioxide).
- **Incorrect Options**: A (Flow of heat from colder to warmer body) and B (Gas in a container contracting in one corner).

### Final Answer:
The processes which occur spontaneously are:
- C: Gas expanding to fill the available volume.
- D: Burning of carbon in oxygen to give carbon dioxide.